SOLUTION: The cost C in pesos of operating a certain wood-cutting machine is related to the number of minutes n the machine is run by the function C(n) = 2.2n^2 - 66n + 655. For what number

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: The cost C in pesos of operating a certain wood-cutting machine is related to the number of minutes n the machine is run by the function C(n) = 2.2n^2 - 66n + 655. For what number       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 966145: The cost C in pesos of operating a certain wood-cutting machine is related to the number of minutes n the machine is run by the function C(n) = 2.2n^2 - 66n + 655. For what number of minutes is the cost of running the machine a minimum? What is the minimum cost?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
2.2n^2 - 66n + 655 is a quadratic equation that opens up and points down.

the graph of that equation looks like this:

graph%28400%2C400%2C-50%2C50%2C-1000%2C1000%2C2.2x%5E2-66x%2B655%29}

the minimum point on the graph of that equation is found by the formula:

x = -b/2a

the quadratic formula in standard form is ax^2 + bx + c = 0

just replace n with x and your equation will conform to this convention.

2.2n^2 - 66n + 655 becomes 2.2x^2 - 66x + 655.

since this equation is in standard form, then:

a = 2.2
b = -66
c = 655

x = -b/2a becomes x = 66/4.4 which becomes x = 15

when x = 15, 2.2x^2 - 66x + 655 becomes 2.2(15)^2 - 66(15) + 655 which becomes 160.

the minimum point on the graph is when x = 15 and y = 160.

that can be seen on the same graph with y = 160 added to it as shown below:

graph%28400%2C400%2C-50%2C50%2C-1000%2C1000%2C2.2x%5E2-66x%2B655%2C160%29}

the question is:

For what number of minutes is the cost of running the machine a minimum? What is the minimum cost?

the answer is:

the minimum cost is 160 pesos when the machine has been running for 15 minutes.